Analyzing three-dimensional viscoelasticity problems via the improved element-free Galerkin (IEFG) method

Based on the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method for three-dimensional viscoelasticity problems is presented in this paper. The improved moving least-squares (IMLS) approximation is employed to form the shape function, the Galerkin weak form is employed to obtain the equations system, and the penalty method is used to impose the essential boundary conditions. A differential constitutive relationship is assumed to describe the viscoelasticity behavior, and the traditional Newton–Raphson iteration procedure is selected for the time discretization. Then the formulae of the IEFG method for three-dimensional viscoelasticity problems are obtained. Three numerical examples are given to demonstrate the validity and efficiency of the method in this paper. And the scaling parameter, number of nodes and the time step length are considered for the convergence study. Compared with the element-free Galerkin method, the computational efficiency is improved markedly by using the IEFG method.